Ferreira, Jose T. A. S., Juárez, Miguel A. and Steel, Mark F. J.. (2008) Directional log-spline distributions. Bayesian analysis, Vol.3 (No.2). pp. 297-315. ISSN 1931-6690

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Abstract

We introduce a new class of distributions to model directional data, based on hyperspherical log-splines. The class is very flexible and can be used to model data that exhibit features that cannot be accommodated by typical parametric distributions, such as asymmetries and multimodality. The distributions are defined on hyperspheres of any dimension and thus, include the most common circular and spherical cases. Due to the flexibility of hyperspherical log-splines, the distributions can closely approximate observed behaviour and are as smooth as desired. We propose a Bayesian setup for conducting inference with directional log-spline distributions where we pay particular attention to the prior specification and the matching of the priors of the log-splines model and an alternative model constructed through a mixture of von Mises distributions. We compare both models in the context of three data sets: simulated data on the circle, circular data on the movement of turtles and a spherical application to the arrival direction of cosmic rays.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Distribution (Probability theory), Bayesian statistical decision theory
Journal or Publication Title:	Bayesian analysis
Publisher:	Int Soc Bayesian Analysis
ISSN:	1931-6690
Date:	2008
Volume:	Vol.3
Number:	No.2
Number of Pages:	19
Page Range:	pp. 297-315
Identification Number:	10.1214/08-BA311
Status:	Peer Reviewed
Publication Status:	Published
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	GR/T17908/01 (EPSRC)
URI:	http://wrap.warwick.ac.uk/id/eprint/28867

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